The present invention relates to mapping subsurface hydraulic conductivity, particularly to the use of Electrical Impedance Tomography (EIT) for mapping subsurface hydraulic conductivity, and more particularly to using Electrical Resistance Tomography (ERT) to characterize and map hydraulic conductivity using measurements of both amplitude and complex phase, thus generalizing ERT to EIT.
ERT has been established as a useful tool for imaging electrical conductivity variations in the earth. The source field is established through current injection using electrodes inserted into the ground. The current is often injected via electrodes in one borehole, while the measured changes in electrical potential are observed in another, distant borehole. However, the method may also be used successfully in combination with surface sources and/or receivers. The goal of the ERT procedure is to image electrical conductivity variations in the earth, much as x-ray tomography is used in image density variations through cross-sections of the body. Although the electrical conductivity is a particularly useful quantity to measure, nevertheless it is often not the conductivity that one really wants to measure. Other parameters of the underground environment are of more direct interest, such as porosity, fluid saturation, and hydraulic conductivity. ERT has also been shown to be effective in measuring/inferring temperatures underground, see U.S. Pat. No. 5,346,307, issued Sep. 13, 1994, to A. L. Ramirez et al.
Electrical logging has long been used in the petroleum and environmental industries to measure the electrical conductivity in the region surrounding a borehole. This data, which is used to estimate pore-fluid saturations near a well, is very sensitive to variations in rock pore fluid. Mapping near-surface variation of conductivity has also been found to be a very sensitive indicator of zones of higher salinity and acidity in many shallow environmental studies.
Recent research at the Lawrence Livermore National Laboratory (LLNL) and elsewhere has developed instrumentation and software to deploy ERT imaging capabilities in both crosshole and surface-to-borehole configurations, thereby extending the conductivity information to the region between boreholes. Both 2-D and 3-D images have been successfully obtained and used to monitor both conductive and resistive plumes of fluid contaminants. The results have shown that subsurface conductivity is determined at a much higher resolution than can be achieved with surface techniques alone and much greater penetration than can be achieved with ground penetrating radar (GPR) technology.
There have been many attempts to relate hydraulic conductivity (also called fluid permeability or Darcy's constant) to electrical conductivity and/or formation factor measurements in rocks. It is well known that these efforts have had only very limited success. The physical reason for this lack of success is related to the fact that electrical conductivity is a scale-invariant property of the porous medium, just as the porosity is a scale-invariant property. This fact means that it could be possible (at least in principle) to relate these two scale-invariant properties, and the resulting well-known relation is Archie's law giving formation factor as a power of porosity. See G. E. Archie, "The Electrical Resistivity Log as an Aid in Determining Some Reservoir Characteristics," Trans. AIME, 146, 54-62, 1942. On the other hand, it is also well known that the permeability is not a scale-invariant property. The permeability depends not only on the porosity but also on the grain size (or pore size or throat size, if you prefer). Grain size distribution is a property that varies with scale. Thus at least two measurements are needed to specify permeability; formation factor or porosity by themselves are not sufficient to determine the permeability-not even in principle. The second measurement that is required is one that determines an appropriate length scale.
There has been considerable effort in recent years to show that a length scale pertinent for porous media can be determined in principle by using electrical measurements alone. See Johnson, et al., 1986 (D. L. Johnson, et al., New Pore-Size Parameter Characterizing Transport in Porous Media, Phys. Rev. Lett., 57, 2564-2567, 1986), Johnson et al., 1987 (D. L. Johnson et al., Theory of Dynamic Permeability and Tortuosity in Fluid-Saturated Porous Media, J. Fluid Mech., 176, 379-402, 1987), and Avellaneda et al., 1991 (M. Avellaneda et al., Rigorous Link Between Fluid Permeability, Electrical Conductivity, and Relaxation Times for Transport in Porous Media, Phys. Fluids A, 3, 2539-2540, 1991). However, these methods require more information than is usually available for a given situation in the field. For example, to use the ideas of Johnson et al. (1986) requires a series of experiments using saturating fluids at different levels of salinity, which is impractical for field applications. A somewhat more promising approach has been suggested by Borner et al., 1996 (F. D. Borner et al., Evaluation of Transport and Storage Properties in the Soil and Groundwater Zone from Induced Polarization Measurements, Geophys. Prospecting, 44, 583-601, 1996) in which complex electrical conductivity measurements (i.e., frequency-dependent measurements including both amplitude and phase) provide the two pieces of information required to determine the permeability. The physical principles underlying the analysis in the approach of Borner et al. (1996) are not as well-founded, however, as is that of the earlier references already mentioned.
The present invention will broaden the applicability of the ERT method to include measurements of hydraulic conductivity. The invention combines theoretical and experimental results to characterize and map hydraulic conductivity using measurements of both amplitude and complex phase, thus generalizing ERT to EIT. Hydraulic conductivity is known to be logistically difficult and expensive to measure by virtually all existing methods. Yet this important parameter controls the ability to flush unwanted contaminants from the ground or to extract commercially desirable fluids, such as oil and gas, from underground reservoirs. Inexpensive maps of hydraulic conductivity, even if relatively crude ones, will be of great help in improving planning strategies for the subsequent remediation efforts or for reservoir exploitation.
As pointed out above, both 2-D and 3-D images can be successfully obtained and used to monitor both conductive and resistive plumes of fluid contaminants, and the results have shown that subsurface conductivity is determined at a much higher resolution than can be achieved with surface techniques alone and much greater penetration than can be achieved with GPR technology. Utilizing the present invention, similar results for hydraulic conductivity can be achieved by making 3-D maps based on ERT/EIT data. This invention is a major advance both in terms of economy and in terms of imaging capability, because current methods of imaging hydraulic conductivity generally obtain only averages with fairly narrow layers rather than true localized hydraulic conductivity measurements. The present invention involves making complex electrical conductivity measurements in a manner similar to that suggested by Borner et al. (1996), but to analyze those results in terms of the so-called "lambda parameter" of Johnson et al. (1986; 1987). The lambda parameter (.LAMBDA.) is a direct measure of the appropriate length scale of the porous medium; i.e., the scale pertinent to fluid flow. The analysis shows the required two parameters (for example, .LAMBDA. and electrical conductivity .sigma.) can be obtained by examining both amplitude and phase in a frequency-dependent electrical conductivity measurement.